An opaque sphere of radius R lies on a horizontal plane. On the perpendicular through the point of contact there is a point source of light a distance R above the sphere then area of shadow on the plane is

Q. A hollow sphere of radius $R$ lies on a smooth horizontal surface. It is pulled by a horizontal force acting tangentially from the highest point. The distance traveled by the sphere during the time it makes one full rotation is

Q. A sphere of radius $r$ is lying on a ground. The sphere makes an angle of measure $60$ at a point $A$ on the ground, then the distance of the center of the sphere form $A$ is

Q. An opaque sphere of radius $a$ is just immersed in a transparent liquid as shown in figure. A point source is placed on the vertical diameter of the sphere at a distance $\frac{a}{2}$ from the top of the sphere. A ray from the point source after refraction from the air liquid interface forms tangent to the sphere. The angle of refraction for that particular ray is ${30}^{\circ }$. The refractive index of the liquid is

Q. A uniform sphere of radius $R$ is placed on a smooth horizontal surface and a horizontal force $F$ is applied on it at a distance $h$ above the centre. The acceleration of the centre of mass of the sphere is

Q. A sphere is rolling without slipping on a fixed horizontal plane surface. In the figure, $A$ is the point of contact, $B$ is the centre of the sphere and $C$ is its topmost point. Then,